One of the main results of the Fermi Gamma-Ray Space Telescope is the discovery of gamma-ray selected pulsars. The high magnetic field pulsar, PSR J0007+7303 in CTA1, was the first ever to be discovered through its gamma-ray pulsations. Based on analysis of 2 years of LAT survey data, we report on the discovery of I-ray emission in the off-pulse phase interval at the approx. 6sigma level. The flux from this emission in the energy range E > or =::: 100 MeV is F(sub 100) = (1.73+/-0.40) x 10(exp -8) photons/sq cm/s and is best fitted by a power law with a photon index of Gamma = 2.54+/-0.14. The pulsed gamma-ray flux in the same energy range is F(sub 100) = (3.95+/-0.07) x 10(exp -7) photons/sq cm/s and is best fitted by an exponentially-cutoff power-law spectrum with a photon index of Gamma = 1.41+/-0.23 and a cutoff energy E(sub c) = 4.04+/-0.20 GeV. We find no flux variability neither at the 2009 May glitch nor in the long term behavior. We model the gamma-ray light curve with two high-altitude emission models, the outer gap and slot gap, and find that the model that best fits the data depends strongly on the assumed origin of the off-pulse emission. Both models favor a large angle between the magnetic axis and observer line of sight, consistent with the nondetection of radio emission being a geometrical effect. Finally we discuss how the LAT results bear on the understanding of the cooling of this neutron star.